Spending it faster: What a 10,000-agent proof means for AI’s borrowed expertise

On Sept. 8, OpenAI announced that an unreleased internal model had produced a proposed solution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems—a set of complex, unsolved problems selected by the Clay Mathematics Institute in 2000 that offer a $1 million prize for the first correct solution for each.

Roughly 10,000 agents ran in parallel for 88 hours. The compute bill ran millions of dollars, which OpenAI’s Sébastien Bubeck described in the press briefing as roughly a thousand times what the company had previously spent on a single problem.

The proof is not verified. Mathematicians are reading it now, and under Clay’s rules a proposed solution must appear in a qualifying publication, wait two years, and win general acceptance in the field before the prize is considered at all. OpenAI says it does not intend to claim it.

That was five weeks ago, and it is already the smaller story. On Oct. 6, OpenAI released 722 manuscripts in a single GitHub drop, claiming progress on 372 open problems across algebra, geometry, number theory, and theoretical computer science, all produced by the same unreleased internal model. The company estimates the average result cost roughly three hours of ChatGPT Pro compute. Only 162 of the manuscripts arrived with the machine-checkable Lean formalizations that let a computer confirm a proof, and mathematicians pushed back immediately: A group calling itself the Association for Human Mathematics described the release as “not a demonstration of scholarship, but a demonstration of power.” A day later, OpenAI withdrew three of the manuscripts after an internal audit caught a sign error that invalidated one argument and the constructions in two papers that depended on it.

Assume the Navier-Stokes proof holds. What it demonstrates is the pattern I described in July 2026: Generative artificial intelligence (AI) is exceptionally well-suited to normal science, the puzzle-solving work inside a frame that people have already built. In this case, the frame was built by other people a long time ago.

What is new is the scale, and the scale changes the problem. Ten thousand agents working on well-posed questions for four days is a different kind of instrument. So is a model that can mint 700 papers at three hours of compute apiece. Together they move the binding constraint on science from the production of results to the absorption of them, and the policy agenda I set out in July is missing the instrument that matters most for that. The important part is not the proof. It is the mismatch the proof exposes: We are about to have far more machine-generated science than people qualified to evaluate it, there is no institution for verifying machine-generated claims outside pure mathematics, and the training pipeline that produces qualified evaluators is being cut at exactly the wrong moment.

Nothing in that agent swarm decided that fluid singularities were worth 90 years of attention. The problem came to the swarm already framed, with a clean statement and an unambiguous success criterion. This is the most favorable possible terrain for a system that excels at search inside a well-specified frame.

Bubeck said OpenAI began working on the Millennium problems because of viral Twitter rumors that Anthropic had resolved two of them. The agenda was set by competitive anxiety about a rival lab. Whatever else that is, it is not a machine identifying an important question.

The telescope reading

When Galileo pointed a telescope at Jupiter in 1610 and found four moons, the instrument did not settle the questions astronomers already had. It generated new ones faster than anyone could work through them, and the number of working astronomers went up.

An agent swarm that can spend $10 million on inference for a single conjecture is an instrument of that kind. It reaches places unaided human cognition cannot, and it will return results nobody asked for and that nobody yet understands. The optimistic reading of this week is that we have acquired a very powerful telescope.

The pessimistic reading is that we have acquired it at a moment when we are cutting the number of astronomers.

Here is the asymmetry that should organize the policy response.

The production of new results is now a scalable industrial process: add agents, add compute, add hours, get more output. The unit cost falls every year, and the parallelism has no obvious ceiling. Bubeck framed the implication as a question for the audience: What happens when organizations can spend that kind of compute on problems they actually care about? The October release was a preview of the answer: 722 manuscripts in one day, most of them without formal verification.

Absorption does not scale. Understanding a result is a change in a person. It happens one person at a time, at a rate bounded by human cognition and by years of prior training. The internet made information nearly free and did not make doctorates meaningfully shorter. AI tutoring helps, and I have cited a Harvard physics trial before as the best causal evidence we have: Students with a purpose-built tutor learned roughly twice as much as students in an active-learning classroom, in less time. Twice is a real gain; it is not 10,000 agents in parallel.

The ratio of results produced to results understood therefore rises with every capability improvement. This is ordinary economics. When one input becomes abundant, the marginal value of its complement rises. AI substitutes for research labor and complements absorption labor, and absorption is becoming the binding constraint on what science actually delivers.

In July, I leaned on Fabrizio Dell’Acqua and colleagues’ field experiment, which found that consultants using AI on a task outside its capability frontier performed about 19 percentage points worse because the model produced confident-sounding answers and the users lacked the expertise to detect them. The diagnostic point was that the user generally cannot tell which side of the frontier a task falls on. That problem has now arrived at the top of the skill distribution, and mathematicians have started saying so themselves.

The clearest evidence is from May, when an internal OpenAI model disproved Paul Erdős’ unit distance conjecture, an 80-year-old problem in discrete geometry. The company did not publish the proof alone. Nine mathematicians checked it and published a companion paper alongside it, which they describe in their own abstract as a short, digested, human-verified version of the machine’s argument, together with individually signed reflections on what it means.

Read that paper and the division of labor is unmistakable. The proof did not need rescuing. Thomas Bloom applied the test that matters for my argument, asking whether the result taught the field anything new and answering with a qualified yes: Number-theoretic constructions have more to say about these questions than anyone suspected, though the proof introduces no new geometric tools of the kind a proof of the conjecture would have required. Bloom then makes the point directly. The original AI proof was completely valid, and humans improved it substantially anyway, because the work of discussing, digesting, and improving a proof and drawing out its consequences remains theirs.

Two of the reflections should worry anyone assuming this layer will hold. Victor Wang noted that verification went smoothly because the digested argument ran only a few pages, and that a longer one might have gone differently, since the participants may have been less willing to spend the time. The check held because nine busy people volunteered and the reading was short. Melanie Matchett Wood put the jagged frontier in its sharpest form: In many cases it will be easier for AI to convince mathematicians it has a proof than to produce a correct argument, and she does not think the profession is prepared for that.

The Navier-Stokes episode shows the same layer operating under worse conditions. There is no companion paper. It was Tristan Buckmaster at New York University who recognized, from one word in a text message, that the smooth-forcing route was the obscure path he and Levent Alpöge had been walking, and who published a careful statement that stopped short of alleging anything. I take no position on that dispute. My point is narrower: The people positioned to notice there was anything to examine were two mathematicians who happened to be working on the same problem.

William Thurston made the underlying case in a 1994 essay that mathematicians still argue about. The discipline’s output, he wrote, is not a stock of proven statements but ways for people to understand and think about mathematics. The nine authors of that companion paper were doing exactly what he described, and they had to be assembled by hand to do it.

The second reason to care about absorption is that knowledge sitting unread does very little.

Lawrence Craven, a general practitioner in Glendale, California, noticed around 1950 that his tonsillectomy patients who chewed aspirin gum bled more, reasoned that aspirin might therefore prevent the clots behind heart attacks, put several thousand of his male patients on a daily dose, and reported that none of them had one. He published in obscure journals, was ignored because he had no randomized evidence, and died of a heart attack in 1957. The finding sat for 20 years. Then John Vane showed in 1971 that aspirin blocks prostaglandin synthesis. The mechanism explained which patients would benefit and at what dose, and that understanding is what launched the trials that turned an ignored observation into one of the cheapest effective interventions in medicine.

Institutions reinforce this. Licensure, liability, regulatory approval, and peer review all run through a person who can be questioned and held responsible. A Food and Drug Administration reviewer signs. A licensed engineer stamps the drawing. You cannot operate those mechanisms on outputs that no accountable human comprehends, and rebuilding them so no human understanding is required would be a far larger undertaking than anything currently under discussion.

The July argument returns here in its sharpest form.

The people who can check frontier work are produced by doing frontier work. There is no consumption-only path to that competence. It comes through apprenticeship: proof search, literature review, replication, reconstruction of other people’s arguments. Graduate training manufactures absorptive capacity as a byproduct of doing the research yourself.

That apprenticeship work is precisely what agents now perform faster and cheaper. The seniority-biased hiring I documented in firms has a direct analogue in the laboratory, and the logic is identical: Paying a graduate student to do work an agent completes in an afternoon will start to look indefensible to a department chair long before anyone notices what has been lost. In July, I called this spending an inheritance. The Navier-Stokes result means we are now spending it faster, because the volume of machine-generated science requiring human evaluation is rising at the same time that the number of qualified evaluators is falling.

The economics do not self-correct. Verification is a public good. It is nonrival, and a department that trains a competent skeptic captures almost none of the value that person later creates by catching someone else’s error. The private incentive to produce absorbers is weakest exactly when their social value is highest.

In July, I proposed four things: sequencing in K-12 education, AI-free assessment at credentialing stages, research funding instruments that can distinguish novelty from recombination, and procurement standards for pedagogical AI. I would now add a fifth, and I would put it first.

We have no institution for verifying machine-generated scientific claims outside of pure mathematics.

Mathematics is the fortunate case. Programs provide mechanical checking, and Clay’s two-year publication-and-acceptance requirement is an explicit, deliberately slow human verification process. Nothing equivalent exists in biology, materials science, or clinical research, where AI systems are already generating candidate results at volume and where there is no formal verifier at all. The check in those fields is peer review, which is unpaid, already overloaded, and staffed by exactly the senior cohort that is aging out. OpenAI itself appears to see the gap: alongside the October release, it said it will fund workshops, conferences, and special programs “around the understanding of major results produced by AI.” A lab paying for the absorption of its own output is welcome. It is also the clearest statement available that no public institution exists to do the job.

The general principle is that verification should be treated as a first-class research activity rather than as unpaid service, and that federal training support should be justified by the evaluative capacity it produces rather than by the papers the trainees will write. The papers are about to be cheap. The evaluative capacity is not.

That last point cuts against how the case is currently made and how it is currently being decided. The National Science Foundation’s (NSF) Graduate Research Fellowship Program collapsed in 2025, rebounded to nearly 2,600 awards in April 2026, and the agency’s own solicitation now expects 1,500 next year, with the fiscal year 2027 request proposing just over a 40% cut. Defenders of that program have generally argued that the fellows produce valuable research. That argument is genuinely weaker this month than it was last month, and we should stop making it.

The concrete version of the alternative is not complicated. Congress should reverse the FY 2027 reduction and restore the fellowship program to at least its 2026 level. Additionally, the NSF should attach an evaluative track to a share of the awards, in which fellows spend part of their training independently reproducing and digesting machine-generated results in their field, with the digested version counting as a funded deliverable rather than as service. The NSF and the National Institutes of Health should stand up paid verification teams on the model those nine mathematicians improvised in May and should require any federally funded project that builds on AI-generated findings to budget for independent checking of them. The mathematicians wrote their companion paper because they were willing to spend the time. Willingness is not a policy instrument.

The magnitudes here are worth holding side by side. One laboratory spent millions of dollars on compute for a single conjecture in September, a thousand times what it had spent on any problem before. Keeping in existence the small number of people who can tell the rest of us whether that answer means anything costs a rounding error against the price of generating it, and it is the only part of the enterprise that money cannot buy back quickly.

The argument that survives is that we are about to have far more machine-generated science than we have people qualified to evaluate it. The pipeline that produces those people takes a decade to refill. It takes about three years to break.